I think the most commonly used is the 55 grain FMJ for plinking as it seems the easiest and cheapest to acquire with all the surplus ammo available.
I don't use the .223 for hunting but expect that the soft points would be more common for that. The heavier bullets (62 to 69 grain) tend to deliver more energy when they hit although some drop significant velocity if that is a concern to you.
Those NEF single shots are very nice and extremely reliable rifles. I grew up using their 45-70 version and loved it to death. Their shotguns are nice too but boy do they do a job on my shoulder.
Congratulations to you and your daughter!